29 resultados para Non-autonomous dynamical systems
Resumo:
According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.
Resumo:
We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.
Resumo:
We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.
Resumo:
Current conceptual models of reciprocal interactions linking soil structure, plants and arbuscular mycorrhizal fungi emphasise positive feedbacks among the components of the system. However, dynamical systems with high dimensionality and several positive feedbacks (i.e. mutualism) are prone to instability. Further, organisms such as arbuscular mycorrhizal fungi (AMF) are obligate biotrophs of plants and are considered major biological agents in soil aggregate stabilization. With these considerations in mind, we developed dynamical models of soil ecosystems that reflect the main features of current conceptual models and empirical data, especially positive feedbacks and linear interactions among plants, AMF and the component of soil structure dependent on aggregates. We found that systems become increasingly unstable the more positive effects with Type I functional response (i.e., the growth rate of a mutualist is modified by the density of its partner through linear proportionality) are added to the model, to the point that increasing the realism of models by adding linear effects produces the most unstable systems. The present theoretical analysis thus offers a framework for modelling and suggests new directions for experimental studies on the interrelationship between soil structure, plants and AMF. Non-linearity in functional responses, spatial and temporal heterogeneity, and indirect effects can be invoked on a theoretical basis and experimentally tested in laboratory and field experiments in order to account for and buffer the local instability of the simplest of current scenarios. This first model presented here may generate interest in more explicitly representing the role of biota in soil physical structure, a phenomenon that is typically viewed in a more process- and management-focused context. (C) 2011 Elsevier Ltd. All rights reserved.
Resumo:
The Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a non-intrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations.
Resumo:
This chapter examines key concepts with respect to cancer gene therapy and the current issues with respect to non-viral delivery. The biological and molecular barriers that need to be overcome before effective non-viral delivery systems can be appropriately designed for oncology applications are highlighted and ways to overcome these are discussed. Strategies developed to evade the immune response are also described and targeted gene delivery is examined with the most effective strategies highlighted. Finally, this chapter proposes a new way forward based on a growing body of evidence that supports a multifunctional delivery approach involving the creation of vectors, with a unique molecular architecture designed using a bottom-up approach.
Resumo:
We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.
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We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.
Resumo:
Modelling and control of nonlinear dynamical systems is a challenging problem since the dynamics of such systems change over their parameter space. Conventional methodologies for designing nonlinear control laws, such as gain scheduling, are effective because the designer partitions the overall complex control into a number of simpler sub-tasks. This paper describes a new genetic algorithm based method for the design of a modular neural network (MNN) control architecture that learns such partitions of an overall complex control task. Here a chromosome represents both the structure and parameters of an individual neural network in the MNN controller and a hierarchical fuzzy approach is used to select the chromosomes required to accomplish a given control task. This new strategy is applied to the end-point tracking of a single-link flexible manipulator modelled from experimental data. Results show that the MNN controller is simple to design and produces superior performance compared to a single neural network (SNN) controller which is theoretically capable of achieving the desired trajectory. (C) 2003 Elsevier Ltd. All rights reserved.
Resumo:
The dilute acid hydrolysis of grass and cellulose with phosphoric acid was undertaken in a microwave reactor system. The experimental data and reaction kinetic analysis indicate that this is a potential process for cellulose and hemi-cellulose hydrolysis, due to a rapid hydrolysis reaction at moderate temperatures. The optimum conditions for grass hydrolysis were found to be 2.5% phosphoric acid at a temperature of 175 degrees C. It was found that sugar degradation occurred at acid concentrations greater than 2.5% (v/v) and temperatures greater than 175 degrees C. In a further series of experiments, the kinetics of dilute acid hydrolysis of cellulose was investigated varying phosphoric acid concentration and reaction temperatures. The experimental data indicate that the use of microwave technology can successfully facilitate dilute acid hydrolysis of cellulose allowing high yields of glucose in short reaction times. The optimum conditions gave a yield of 90% glucose. A pseudo-homogeneous consecutive first order reaction was assumed and the reaction rate constants were calculated as: k(1) = 0.0813 s(-1); k(2) = 0.0075 s(-1), which compare favourably with reaction rate constants found in conventional non-microwave reaction systems. The kinetic analysis would indicate that the primary advantages of employing microwave heating were to: achieve a high rate constant at moderate temperatures: and to prevent 'hot spot' formation within the reactor, which would have cause localised degradation of glucose.
Resumo:
Reliable population DNA molecular markers are difficult to develop for molluscs, the reasons for which are largely unknown. Identical protocols for microsatellite marker development were implemented in three gastropods. Success rates were lower for Gibbula cineraria compared to Littorina littorea and L. saxatilis. Comparative genomic analysis of 47.2?kb of microsatellite containing sequences (MCS) revealed a high incidence of cryptic repetitive DNA in their flanking regions. The majority of these were novel, and could be grouped into DNA families based upon sequence similarities. Significant inter-specific variation in abundance of cryptic repetitive DNA and DNA families was observed. Repbase scans show that a large proportion of cryptic repetitive DNA was identified as transposable elements (TEs). We argue that a large number of TEs and their transpositional activity may be linked to differential rates of DNA multiplication and recombination. This is likely to be an important factor explaining inter-specific variation in genome stability and hence microsatellite marker development success rates. Gastropods also differed significantly in the type of TEs classes (autonomous vs non-autonomous) observed. We propose that dissimilar transpositional mechanisms differentiate the TE classes in terms of their propensity for transposition, fixation and/or silencing. Consequently, the phylogenetic conservation of non-autonomous TEs, such as CvA, suggests that dispersal of these elements may have behaved as microsatellite-inducing elements. Results seem to indicate that, compared to autonomous, non-autonomous TEs maybe have a more active role in genome rearrangement processes. The implications of the findings for genomic rearrangement, stability and marker development are discussed.